Simplify the following expression: $z = \dfrac{t^2 - 15t + 56}{t - 8} $
Solution: First factor the polynomial in the numerator. $ t^2 - 15t + 56 = (t - 8)(t - 7) $ So we can rewrite the expression as: $z = \dfrac{(t - 8)(t - 7)}{t - 8} $ We can divide the numerator and denominator by $(t - 8)$ on condition that $t \neq 8$ Therefore $z = t - 7; t \neq 8$